Factoring the polynomial [tex]4x^4-20x^2-3x^2 + 15[/tex] by grouping means separation of the polynomial in two addends, each of them consists of two addends:
[tex]4x^4-20x^2-3x^2 + 15=(4x^4-20x^2)+(-3x^2+15).[/tex]
In first brackets the common factor is [tex]4x^2,[/tex] in second brackets the common factor is [tex]-3.[/tex]
Then
[tex](4x^4-20x^2)+(-3x^2+15)=4x^2(x^2-5)-3(x^2-5)=(x^2-5)(4x^2-3).[/tex]
Answer: correct choice is B
Since the factor of the polynomial [tex]\rm 4x^4 -20x^2-3x^2 + 15\\[/tex] is [tex]\rm(x^2-5)(4x^2 - 3)\\[/tex].
Thus, the correct option is B.
Polynomial is an algebraic expression that consists of variables and coefficients. Variable are called unknown. We can apply arithmetic operations such as addition, subtraction, etc. But not divisible by variable.
Given
The polynomial is [tex]\rm 4x^4 -20x^2-3x^2 + 15\\[/tex].
To find
The factors of the polynomial.
Simplify, the polynomial.
[tex]\rm 4x^4 -23x^2 + 15\\[/tex]
On factorizing, we get
[tex]\rm 4x^4 -20x^2-3x^2 + 15\\\\\rm 4x^2(x^2 - 5) -3(x^2 -5) \\\\\rm (x^2-5)(4x^2 - 3)\\[/tex]
Since the factor of the polynomial [tex]\rm 4x^4 -20x^2-3x^2 + 15\\[/tex] is [tex]\rm(x^2-5)(4x^2 - 3)\\[/tex].
Thus, the correct option is B.
More about the polynomial link is given below.
https://brainly.com/question/17822016
